Probabilistic Foundations of Machine Learning, Volume I: Probability, Statistics, and Distributions with Python – Paperback

This textbook addresses a common gap in modern AI and machine learning education: many students can build powerful models without fully understanding the probabilistic and statistical principles that underlie them. While modern machine learning is often introduced through algorithms, a deeper understanding requires the statistical principles that explain why those algorithms work, when they can be trusted, and how they generalize beyond the observed data. This book is the first volume of a two-volume series.

Volume I, Probability, Statistics, and Distributions with Python, develops the foundations of uncertainty through descriptive statistics, probability theory, random variables, transformations, expectation, computational sampling, core distribution families, multivariate probability, and high-dimensional phenomena.

Volume II, Inference, Learning, and Optimization with Python, develops statistical inference through expectation, estimation, hypothesis testing, and linear regression; extends these ideas to Bayesian learning and computational inference; establishes the foundations of machine learning through risk, loss, generalization, and learning theory; and concludes with optimization methods for modern machine learning and deep learning.

This two-volume series is mainly intended for undergraduate and graduate students in computer science, data science, statistics, electrical engineering, and related fields. It assumes basic algebra and Python familiarity at the beginning. Later chapters gradually require more comfort with calculus, linear algebra, and mathematical notation. No measure-theoretic background is assumed.